Peter Hussey, Samuel Wertheimer, and Ateev Mehrotra conducted a systematic review of the association between health care cost and quality (both variously measured) that included 61 studies. It’s published in the latest issue of the Annals of Internal Medicine.
The findings of the association between health care cost and quality were inconsistent, with 21 studies (34%) reporting a positive or mixed-positive association (higher cost associated with higher quality); 18 studies (30%) reporting a negative or mixed-negative association (lower cost associated with higher quality); and 22 studies (36%) reporting no difference (1 study), an imprecise or indeterminate association (8 studies), or mixed association (13 studies).
Of the 61 included studies, 9 (15%) used instrumental variables analysis to address confounding by unobserved patient health status. Seven of the 9 studies (78%) reported a positive cost-quality association and 2 had mixed findings.
And, overall, they “found inconsistent evidence on  the magnitude of the association between health care costs and quality.”
So, if you’re inclined to think the instrumental variables studies are the strongest methodologically, you might believe that the cost-quality correlation is positive and even causal. In general, that is what I believe, though I have not carefully read all the studies. (Here’s one of many posts on why I think this in spite of the studies that suggest otherwise.) But, if you view the literature as a whole, the state of knowledge seems less certain. I don’t think it’s sensible to not take into consideration methodological strength among other factors, but that is how some people view these things.
None of my comments above have any bearing on the efficiency of spending. The cost-quality correlation may be positive, but it is not always and everywhere large.